Crosstalk (or inter-channel interference) is a major source of channel impairment for Multiple Input Multiple Output (MIMO) wired communication systems, such as Digital Subscriber Line (DSL) communication systems.
As the demand for higher data rates increases, DSL systems are evolving toward higher frequency bands, wherein crosstalk between neighboring transmission lines (that is to say transmission lines that are in close vicinity over part or whole of their length, such as twisted copper pairs in a cable binder) is more pronounced (the higher frequency, the more coupling).
Different strategies have been developed to mitigate crosstalk and to maximize effective throughput, reach and line stability. These techniques are gradually evolving from static or dynamic spectral management techniques to multi-user signal coordination (or vectoring).
One technique for reducing inter-channel interference is joint signal precoding: the transmit data symbols are jointly passed through a precoder before being transmitted over the respective communication channels. The precoder is such that the concatenation of the precoder and the communication channels results in little or no inter-channel interference at the receivers.
A further technique for reducing inter-channel interference is joint signal post-processing: the receive data symbols are jointly passed through a postcoder before being detected. The postcoder is such that the concatenation of the communication channels and the postcoder results in little or no inter-channel interference at the receivers.
The choice of the vectoring group, that is to say the set of communication lines, the signals of which are jointly processed, is rather critical for achieving good crosstalk mitigation performances. within a vectoring group, each communication line is considered as a disturber line inducing crosstalk into the other communication lines of the group, and the same communication line is considered as a victim line receiving crosstalk from the other communication lines of the group. Crosstalk from lines that do not belong to the vectoring group is treated as alien noise and is not canceled.
Ideally, the vectoring group should match the whole set of communication lines that physically and noticeably interact with each other. Yet, local loop unbundling on account of national regulation policies and/or limited vectoring capabilities may prevent such an exhaustive approach, in which case the vectoring group would include a sub-set only of all the physically interacting lines, thereby yielding limited vectoring gains.
Signal vectoring is typically performed within a Distribution Point Unit (DPU), wherein all the data symbols concurrently transmitted over, or received from, all the subscriber lines of the vectoring group are available. For instance, signal vectoring is advantageously performed within a Digital Subscriber Line Access Multiplexer (DSLAM) deployed at a Central office (co) or as a fiber-fed remote unit closer to subscriber premises (street cabinet, pole cabinet, etc). Signal precoding is particularly appropriate for downstream communication (toward customer premises), while signal post-processing is particularly appropriate for upstream communication (from customer premises).
Linear signal precoding and post-processing are advantageously implemented by means of matrix products.
For instance, a linear precoder performs a matrix-product of a vector of transmit frequency samples with a precoding matrix, the precoding matrix being such that the overall channel matrix is diagonalized, meaning the off-diagonal coefficients of the overall channel, and thus the inter-channel interference, mostly reduce to zero. Practically, and as a first order approximation, the precoder superimposes anti-phase crosstalk pre-compensation signals over the victim line along with the direct signal that destructively interfere at the receiver with the actual crosstalk signals from the respective disturber lines.
Similarly, a linear postcoder performs a matrix-product of a vector of received frequency samples with a crosstalk cancellation matrix, the crosstalk cancellation matrix being such that the overall channel matrix is diagonalized too.
It is of utmost importance thus to get an accurate estimate of the actual crosstalk channels in order to appropriately initialize or update the precoder or postcoder coefficients. In the recommendation entitled “Self-FEKT Cancellation (Vectoring) For Use with VDSL2 Transceivers”, ref. G.993.5, and adopted by the International Telecommunication Union (ITU) on April 2010, the transceiver are configured to send downstream or upstream pilot sequences over the so-called SYNC symbols, which occur periodically after every 256 DATA symbols. In G.993.5 recommendation, it is further assumed that the access node transmits and receives the SYNC symbols over the vectored lines synchronously (super frame alignment) so as pilot signal transmission and interference measurements are carried out synchronously over the respective transmission lines.
On a given victim line, error samples, which comprise both the real and imaginary part of the slicer error (or receive error vector) as measured for a specific SYNC symbol on a per tone or group-of-tones basis are reported to a vectoring controller for further crosstalk estimation. The error samples are correlated with a given pilot sequence transmitted over a given disturber line in order to obtain the crosstalk coupling function from that disturber line. To reject the crosstalk contribution from the other disturber lines, the pilot sequences are made orthogonal to each other, for instance by using Walsh-Hadamard sequences comprising ‘+1’ and ‘−1’ anti-phase symbols. The crosstalk estimates are used for initializing the precoder or postcoder coefficients.
Once the precoder or postcoder coefficients are initialized, the crosstalk coefficients keep on being tracked for any channel variation, as well as for any residual error in the initial estimates of the crosstalk channels. This is typically achieved by means of iterative update methods, such as Least Mean Square (LMS) methods, which gradually converges towards the optimal solution with respect to a given cost function, presently the power of the residual crosstalk signal.
In the idealized linear model, orthogonal pilot sequences as per G.993.5 recommendation are very effective and always produce accurate and unbiased estimates of the crosstalk channels (initialization) or of the residual crosstalk channels (tracking). Yet, due to non-linear effects, the crosstalk estimates can have an undesired offset (or bias) that drives the precoder or postcoder coefficients away from the actual crosstalk channels.
In high crosstalk environments for instance, the sum of the crosstalk vectors from all the pilot sequences transmitted over all the disturber lines can be such that the receive frequency sample goes beyond the decision boundary of the demodulator. As a result, the error vector is reported against the wrong constellation point, yielding an offset in the estimate of the nominal or residual crosstalk channel.
In G.993.5 recommendation, the ideal expected transmit vector is estimated by the receiver. The set of vectors that can be used as pilots is restricted to two states: a normal state (+1) and an inverted state (−1), which is equivalent to Binary Phase Shift Keying (BPSK) modulation. The receiver determines what the transmit vector is expected to be (further referred to as demapping operation) based on determining the most probable half-plane, and this using only information of the specific tone itself. Quadrature Phase Shift Keying (QPSK or 4-QAM) demodulation could alternatively be used for pilot detection, in which case demapping is based on determining the most probable quadrant.
In the event of demapping errors, that is to say when the receiver selects a constellation point different from the transmit constellation point, the reported slicer error has a completely wrong value. This leads to major inaccuracies in the calculation of the crosstalk coupling coefficients, and thus of the precoder and postcoder coefficients, as the vectoring controller is not aware of the fact that a demapping error has occurred within the receiver.
A possible known solution for dealing with demapping errors would be to use multiple demapping decisions across multiple tones. Given that all probe tones in a particular SYNC symbol are all modulated with the same particular bit from of a given pilot sequence, one can use multiple tones to do a joint estimation. This technique is more robust than the straightforward per-tone decision, but in very low Signal to Noise Ratio (SNR) environments, the receiver could still make a wrong decision. If Frequency Dependent Pilot Sequence (FDPS) is used, the technique can still be applied, using the fact that the pilot values repeat periodically after a given number of tones.
Yet, experiments in the field indicate that at least some receiver models keep on using per-tone decision, with either a BPSK or 4-QAM demodulation grid, thereby increasing the likelihood of demapping errors.
Another known solution is the communication of the used pilot sequence to the receiver. The advantage is that the receiver does not need to make a decision anymore. The disadvantage is that sending a message each time in order to change the pilot sequence is cumbersome, introduces delays in the initialization process, and reduces the flexibility for the vectoring controller to change the pilot sequence on the fly.
Still another known solution is the reporting of the full received vector. The advantage is that the receiver does not need to make a decision anymore. However, this solution suffers from a resolution problem: in case of high SNR, one wants to realize a very high cancellation depth. A reduction of the crosstalk to a level below the noise would mean that the error signal will be reduced to very small values compared to the received vector. The most efficient option for error feedback in G.993.5 recommendation makes use of a binary floating point format. As the error vector gets smaller during the convergence process, the exponent decreases, maintaining a constant relative quantization error. Therefore, the absolute quantization error decreases during convergence, even with a small number of bits for error feedback. If the full received vector is to be reported, the word length needs to be such that at the MSB side it can represent the largest direct signal and at the LSB side it can represent the smallest error signal. Therefore, a certain absolute inaccuracy is present. In the last stages of convergence, this absolute quantization error yields a relatively large inaccuracy. To counteract this, many bits would be required to encode the received vector, which would increase the required bandwidth for measurement feedback and thus would reduce the upstream data rate for the end-user.